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Questions tagged [separability]

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21
votes
4answers
4k views

Fast/efficient way to decompose separable integer 2D filter coefficients

I would like to be able to quickly determine whether a given 2D kernel of integer coefficients is separable into two 1D kernels with integer coefficients. E.g. ...
16
votes
3answers
387 views

Is ICA appropriate for separating mixed signals when all source signals are NOT detectable at all sensors?

A generic implementation of ICA for the separation of a mixture of $N$ signals into their $M$ constituent components requires that the signals be assumed to be a linear instantaneous mixture of the ...
7
votes
1answer
3k views

Why does the separable filter reduce the cost of computing the operator?

A separable filter in image processing can be written as product of two more simple filters. Typically a 2-dimensional convolution operation is separated into 2 onedimensional filters. This reduces ...
3
votes
1answer
610 views

How to Check Separability of 2D Signal / Matrix

suppose x(n1,n2) = {1 ,n1=0,n2=0 ; 2 ,n1=1,n2=0 ; 3 ,n1=0,n2=1 ; 6 ,n1=1,n2=1 } then, how do i prove it is separable.
2
votes
2answers
1k views

How Is Laplacian of Gaussian (LoG) Implemented as Four 1D Convolutions?

I am trying to understand the four 1D convolution operations involved in implementation of Laplacian of Gaussian(LoG). I have read this answer and I am also reading ...
2
votes
1answer
603 views

Normalized-cross correlation operation

According to my question about separability of Gabor filters in this link, I want now to convolve my image with this separable filter by using the normalized cross correlation operation. Assume my <...
1
vote
1answer
2k views

How to find out if a transform matrix is separable?

In image processing, when we have a series of basis images, how could we know if the transformation is separable or not? For example, I know that following bases are separable and transformation can ...
1
vote
2answers
5k views

How to Prove a 2D Filter Is Separable?

I want to prove that 2D Gaussian filter is separable and we can separate it into two dimensions, my problem is about the size of filters. we should prove that $G(x,y)*I$(where $G(x,y)=$$\begin{bmatrix}...
1
vote
1answer
2k views

How does a separable filter work?

I am new to signal processing, and was reading about filters. I came upon the sobel filter which has the following forms, From what I understand to apply this filter to a 2-d signal, place the ...
1
vote
1answer
27 views

Separability vs. Resolution - Synonymous terms?

In terms of discrete representation of a variable, let's say time measurements in absolute values in [seconds], is there a difference between separability and resolution? When do speak of either ...
1
vote
0answers
20 views

How to classify overlapped signals?

A known signal, signal 1 got overlapped with an unknown signal. Likewise, signal 2 overlapped with another unknown signal. The problem I face now is how to classify the overlapped signals based on the ...
0
votes
1answer
312 views

Fast/efficient way to compute Laplacian edge enhancement filter

I would like to implement a somewhat smarter Laplacian edge enhancement convolution. Right now it is implemented as (generic 3x3 convolution): ...
0
votes
1answer
220 views

Octave: Poor performance of convolution by separable 1D kernels

As a newbie, I wrote a custom function in octave to perform a 2D image convolution using separable kernels. The results of this custom function were compared with conv2() and they were consistent. But ...